Fuchs introduced purely extending modules as a generalization of extending modules. Ahmed and Abbas gave another generalization for extending modules named semi-extending modules. In this paper, two generalizations of the extending modules are combined to give another generalization. This generalization is said to be almost semi-extending. In fact, the purely extending modules lies between the extending and almost semi-extending modules. We also show that an almost semi-extending module is a proper generalization of purely extending. In addition, various examples and important properties of this class of modules are given and considered. Another characterization of almost semi-extending modules is established. Moreover, the re

The concept of closed quasi principally injective acts over monoids is introduced ,which signifies a generalization for the quasi principally injective as well as for the closed quasi injective acts. Characterization of this concept is intended to show the behavior of a closed quasi principally injective property. At the same time, some properties of closed quasi principally injective acts are examined in terms of their endomorphism monoid. Also, the characterization of a closed self-principally injective monoid is given in terms of its annihilator. The relationship between the following concepts is also studied; closed quasi principally injective acts over monoids, Hopfian, co Hopfian, and directly finite property. Ultimately, based on

The aim of this paper is to introduce the concept of Dedekind semimodules and study the related concepts, such as the class of  semimodules, and Dedekind multiplication semimodules .  And thus study the concept of the embedding of a semimodule in another semimodule. 

    Let R be a commutative ring with unity and let M, N be unitary R-modules. In this research, we give generalizations for the concepts: weakly relative injectivity, relative tightness and weakly injectivity of modules. We call M weakly N-quasi-injective, if for each f  Hom(N,) there exists a submodule X of  such that  f (N)  X ≈ M, where  is the quasi-injective hull of M. And we call M N-quasi-tight, if every quotient N / K of N which embeds in  embeds in M. While we call M weakly quasi-injective if M is weakly N-quasiinjective for every finitely generated R-module N.         Moreover, we generalize some properties of weakly N-injectiv

        Let R be a commutative ring with identity, and let M be a unitary R-module. We introduce a concept of almost bounded submodules as follows: A submodule N of an R-module M is called an almost bounded submodule if there exists xÃŽM, xÏN such that ann_R(N)=ann_R(x).

        In this paper, some properties of almost bounded submodules are given. Also, various basic results about almost bounded submodules are considered.

        Moreover, some relations between almost bounded submodules and other types of modules are considered.

In this paper, we introduce the concept of almost Quasi-Frobcnius fuzzy ring as a " " of Quasi-Frobenius ring. We give some properties about this concept with qoutient fuzzy ring. Also, we study the fuzzy external direct sum of fuzzy rings.

The main goal of this paper is to make link between the subjects of projective
geometry, vector space and linear codes. The properties of codes and some examples
are shown. Furthermore, we will give some information about the geometrical
structure of the arcs. All these arcs are give rise to an error-correcting code that
corrects the maximum possible number of errors for its length.

In this paper We introduce some new types of almost bi-periodic points in topological bitransfprmation groups and thier effects on some types of minimaliy in topological dynamics

    The main aim of this research is to present and to study several basic characteristics of the idea of FI-extending semimodules. The semimodule  is said to be an FI-extending semimodule if each fully invariant subsemimodule of  is essential in direct summand of . The behavior of the FI-extending semimodule with respect to direct summands as well as the direct sum is considered. In addition, the relationship between the singularity and FI-extending semimodule has been studied and investigated. Finally  extending propertywhich is stronger than FI extending,  that  has some results related to FI-extending and singularity is also investigated.

      The concept of semi-essential semimodule has been studied by many researchers.

     In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule  is prime, then  is fully prime. If every semi-essential subsemimodule of -semimodule  is essential then  is fully essential. Finally, a prime subsemimodule  of  is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule  in , if , and whenever  with  is a prime subsemimodule in , , then .  Furthermore, some res